Finite Group Databasebeta

← #10574557

Subgroups — #10574557

Order 512.

5928 conjugacy classes of subgroups.

The subgroup lattice has 845 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62761C211yesmaximal, characteristic
2#60338C214yesmaximal, complemented
3#60337C214yesmaximal, complemented
4#60336C218yesmaximal, complemented
5#60332C214yesmaximal, complemented
6#60331C214yesmaximal, complemented
7#60330C218yesmaximal, complemented
8#60275C214yesmaximal, complemented
9#60267C214yesmaximal, complemented
10#60266C212yesmaximal, complemented
11#60254C214yesmaximal, complemented
12#60249C211yesmaximal, characteristic, complemented
13#60218C214yesmaximal, complemented
14#60206C214yesmaximal, complemented
15#60204C212yesmaximal, complemented
16Q8×#131C214yesmaximal, complemented
17C2×#2960C211yesmaximal, characteristic, complemented
18#3557C414yes—
19#3556C411yescharacteristic
20#3555C414yes—
21#3554C414yes—
22#3553C414yes—
23#3552C414yes—
24#3550C412yes—
25#3548C411yescharacteristic
26#3541C418yes—
27#3531C2214yes—
28#3482C2214yes—
29#3480C2214yes—
30Q8×#41C2214yes—
31#3461C2218yes—
32#3455C2214yes—
33#3444C2212yes—
34C2×#533C2211yescharacteristic
35#2995C2218yes—
36#2995C22116yes—
37#2995C22116yescomplemented
38#2994C22116yes—
39#2994C2218yescomplemented
40#2993C2218yes—
41#2993C22116yes—
42#2993C2218yescomplemented
43#2992C22116yes—
44#2992C22116yescomplemented
45#2991C2214yes—
46#2990C2214yes—
47#2990C2218yescomplemented
48#2989C2218yes—
49#2989C2218yescomplemented
50#2987C2214yes—
51#2987C22116yescomplemented
52#2986C2214yes—
53#2986C2218yescomplemented
54#2985C2218yes—
55#2985C2218yescomplemented
56#2985C22116yescomplemented
57#2984C2218yescomplemented
58#2983C2218yescomplemented
59#2971C2218yescomplemented
60#2969C2218yescomplemented
61#2969C22116yescomplemented
62#2967C22116yes—
63#2967C22116yes—
64#2966C2214yes—
65#2966C2214yes—
66#2966C2214yes—
67#2966C2214yes—
68#2966C22116yes—
69#2966C22116yes—
70#2966C2218yescomplemented
71#2966C22116yescomplemented
72#2965C2214yes—
73#2965C2214yes—
74C8×#41C2214yes—
75C8×#41C2214yes—
76C8×#41C2218yescomplemented
77Q8×M16C2214yes—
78Q8×M16C2214yes—
79Q8×M16C2218yescomplemented
80#2962C2214yes—
81#2962C2218yes—
82#2962C2218yescomplemented
83#2962C22116yescomplemented
84#2961C2214yes—
85#2960C2214yes—
86#2960C2212yes—
87#2960C2212yes—
88#2960C2214yes—
89#2960C2212yes—
90#2960C2212yes—
91#2960C2212yes—
92#2960C2214yes—
93#2960C2212yes—
94#2960C2218yescomplemented
95#2960C22116yescomplemented
96C2×#446C2214yes—
97C2×C8×Q8C2214yes—
98C2×C8×Q8C2218yescomplemented
99#2935C2214yes—
100#2935C2218yes—
101#2932C2214yes—
102#2931C2212yes—
103#2931C2212yes—
104#2931C2214yes—
105#2930C2218yes—
106#2929C2214yes—
107#2929C2214yes—
108#2925C2214yes—
109#2925C2218yes—
110#2923C2218yes—
111#2922C2214yes—
112#2921C2214yes—
113#2920C2212yes—
114#2906C2214yes—
115#2906C2218yes—
116C2×#424C2212yes—
117C2×#423C2211yescharacteristic
118C4×#131C2214yes—
119C4×#131C2218yes—
120C2×#405C2212yes—
121C22×C4×C8C2211yescharacteristic
122C2×#131C2314yes—
123C2×#131C2314yes—
124C2×#131C2318yes—
125C22×M16C2312yes—
126C23×C8C2311yescharacteristic
127C23×C8C2311yescharacteristic
128#564C2×C414yes—
129#563C2×C4116yes—
130#563C2×C418yes—
131#563C2×C4116yes—
132#562C2×C4116yes—
133#562C2×C414yes—
134#559C2×C414yes—
135#559C2×C418yes—
136Q82C2×C414yes—
137#557C2×C414yes—
138#557C2×C418yes—
139#557C2×C414yes—
140#557C2×C414yes—
141#556C2×C414yes—
142#556C2×C418yes—
143#556C2×C418yes—
144#556C2×C414yes—
145#554C2×C418yes—
146#554C2×C4116yes—
147#554C2×C414yes—
148#554C2×C418yes—
149#553C2×C418yes—
150#553C2×C4116yes—
151#552C2×C418yes—
152#552C2×C4116yes—
153#550C2×C414yes—
154D4×Q8C2×C418yes—
155D4×Q8C2×C414yes—
156D4×Q8C2×C414yes—
157#548C2×C418yes—
158#548C2×C418yes—
159#547C2×C418yes—
160#547C2×C414yes—
161#544C2×C418yes—
162#542C2×C418yes—
163#542C2×C418yes—
164#542C2×C418yes—
165#542C2×C4116yes—
166#542C2×C418yes—
167#541C2×C414yes—
168#541C2×C414yes—
169#541C2×C418yes—
170#541C2×C418yes—
171#541C2×C4116yes—
172#540C2×C414yes—
173#540C2×C414yes—
174#539C2×C4116yes—
175#539C2×C4116yes—
176#539C2×C4116yes—
177#538C2×C4116yes—
178#537C2×C418yes—
179#536C2×C418yes—
180#536C2×C418yes—
181#533C2×C411yescharacteristic
182#533C2×C411yescharacteristic
183#533C2×C414yes—
184#533C2×C412yes—
185#533C2×C412yes—
186#533C2×C412yes—
187#533C2314yes—
188#533C2312yes—
189#533C2312yes—
190#533C2312yes—
191#533C2314yes—
192#533C2318yes—
193#533C23116yes—
194#532C2×C412yes—
195#532C2×C412yes—
196#532C2312yes—
197#532C2314yes—
198C2×C4⋊Q8C2×C412yes—
199#529C2×C414yes—
200#529C2×C414yes—
201#529C2×C414yes—
202#529C2×C414yes—
203#529C2314yes—
204#529C2314yes—
205#529C23116yes—
206#529C23116yes—
207#529C2318yes—
208#529C23116yes—
209C2×#125C2×C412yes—
210#525C2×C414yes—
211#525C2×C414yes—
212#525C2314yes—
213C2×C22⋊Q8C2×C414yes—
214C4×#41C2314yes—
215C4×#41C2314yes—
216C4×#41C2318yes—
217C4×#41C2314yes—
218C4×#41C2318yes—
219C2×C4×Q8C2314yes—
220C2×C4×Q8C2318yes—
221C2×#117C2312yes—
222C22×C42C2311yescharacteristic
223#446C2314yes—
224#446C2314yes—
225#446C2314yes—
226#446C2318yes—
227#446C2314yes—
228#446C2318yes—
229#446C2314yes—
230#446C23116yes—
231#446C2314yes—
232#446C2314yes—
233#446C2314yes—
234#446C23116yes—
235#446C23116yes—
236#446C23116yes—
237#446C2318yes—
238#446C23116yes—
239#446C2318yes—
240#446C23116yes—
241#446C23116yes—
242#446C23116yes—
243#446C2318yes—
244#446C23116yes—
245C8×Q8C2314yes—
246C8×Q8C2314yes—
247C8×Q8C2318yes—
248C8×Q8C2318yes—
249C8×Q8C2314yes—
250C8×Q8C2314yes—
251C8×Q8C2314yes—
252C8×Q8C23116yes—
253C8×Q8C2318yes—
254C8×Q8C23116yes—
255C8×Q8C2318yes—
256C8×Q8C2314yes—
257C8×Q8C2314yes—
258C8×Q8C2314yes—
259C8×Q8C2318yes—
260#436C23116yes—
261#436C23116yes—
262#436C2314yes—
263#436C2314yes—
264#436C2314yes—
265#436C2314yes—
266#436C23116yes—
267#436C2318yes—
268#436C23116yes—
269#435C2318yes—
270#435C2318yes—
271#435C2318yes—
272#435C2318yes—
273#435C23116yes—
274#435C23116yes—
275#435C23116yes—
276#435C23116yes—
277#435C23116yes—
278#435C23116yes—
279#435C23116yes—
280C8×D4C2318yes—
281C8×D4C2318yes—
282C8×D4C2318yes—
283C8×D4C2318yes—
284C8×D4C2314yes—
285C8×D4C2314yes—
286C8×D4C2314yes—
287C8×D4C2314yes—
288C8×D4C23116yes—
289C8×D4C2318yes—
290C8×D4C23116yes—
291#433C23116yes—
292#433C23116yes—
293#433C2318yes—
294#433C2318yes—
295#433C23116yes—
296#433C23116yes—
297#433C23116yes—
298#433C23116yes—
299#433C23116yes—
300#432C2314yes—
301#432C2314yes—
302#432C23116yes—
303#432C23116yes—
304#432C23116yes—
305#432C2318yes—
306#431C2314yes—
307#431C2314yes—
308#431C2318yes—
309#431C2318yes—
310#431C2318yes—
311#431C23116yes—
312#424C2318yes—
313#424C2314yes—
314#424C2314yes—
315#424C2314yes—
316#424C2318yes—
317#424C23116yes—
318#424C23116yes—
319#424C23116yes—
320#424C2314yes—
321#423C2314yes—
322#423C2312yes—
323#423C2312yes—
324#423C2312yes—
325#423C2314yes—
326#423C2318yes—
327#423C23116yes—
328#423C2312yes—
329#423C2314yes—
330C2×C4⋊C8C2314yes—
331C2×C4⋊C8C2318yes—
332C2×C4⋊C8C2318yes—
333C2×C4⋊C8C23116yes—
334#408C2314yes—
335#408C2314yes—
336#408C2318yes—
337#407C2314yes—
338#405C2314yes—
339#405C2314yes—
340#405C2314yes—
341#405C2314yes—
342#405C2314yes—
343#405C2314yes—
344#405C2318yes—
345#405C2318yes—
346#405C23116yes—
347#405C2318yes—
348#405C23116yes—
349C4×M16C2314yes—
350C4×M16C2318yes—
351C4×M16C2318yes—
352C4×M16C23116yes—
353C2×#97C2314yes—
354C2×C4×C8C2312yes—
355C2×C4×C8C2312yes—
356C2×C4×C8C2311yescharacteristic
357C2×C4×C8C2312yes—
358C2×C4×C8C2311yescharacteristic
359C2×C4×C8C2312yes—
360C2×C4×C8C2311yescharacteristic
361C2×C4×C8C2311yescharacteristic
362C2×C4×C8C2314yes—
363C2×C4×C8C2318yes—
364C2×C4×C8C23116yes—
365C2×#41C22×C414yes—
366C2×#41C22×C414yes—
367C2×#41C22×C418yes—
368C2×#41C2414yes—
369C22×Q8C22×C414yes—
370C22×Q8C22×C418yes—
371C23×C4C22×C412yes—
372C23×C4C2411yescharacteristic
373#131—216no—
374#131—48no—
375#131—416no—
376C2×M16—44no—
377C2×M16C2414yes—
378C2×M16C2414yes—
379C2×M16C2418yes—
380C2×M16C2414yes—
381C2×M16C2414yes—
382C2×M16C2418yes—
383C2×M16C24116yes—
384C22×C8—24no—
385C22×C8—42no—
386C22×C8C2412yes—
387C22×C8C2411yescharacteristic
388C22×C8C2411yescharacteristic
389C22×C8C2411yescharacteristic
390C22×C8C2414yes—
391C22×C8C2411yescharacteristic
392C22×C8C2411yescharacteristic
393C22×C8C2418yes—
394C22×C8C2411yescharacteristic
395C22×C8C2412yes—
396C22×C8C2411yescharacteristic
397C22×C8C2418yes—
398C22×C8C24116yes—
399C22×C8C2411yescharacteristic
400C4⋊Q8C22×C414yes—
401C4⋊Q8C22×C414yes—
402C4⋊Q8C22×C412yes—
403C4⋊Q8C22×C412yes—
404C4⋊Q8C22×C414yes—
405C4⋊Q8C22×C412yes—
406C4⋊Q8C22×C412yes—
407C4⋊Q8C22×C412yes—
408C4⋊Q8C22×C414yes—
409C4⋊Q8C22×C418yes—
410C4⋊Q8C22×C4116yes—
411C4⋊Q8C22×C418yes—
412C4⋊Q8C22×C418yes—
413C4⋊Q8C22×C4116yes—
414#127C22×C412yes—
415#127C22×C414yes—
416#126C22×C418yes—
417#126C22×C418yes—
418#126C22×C4116yes—
419#126C22×C4116yes—
420#126C22×C4116yes—
421#126C22×C4116yes—
422#126C22×C4116yes—
423#126C22×C4116yes—
424#126C22×C4116yes—
425#125C22×C418yes—
426#125C22×C414yes—
427#125C22×C412yes—
428#125C22×C412yes—
429#125C22×C414yes—
430#125C22×C414yes—
431#125C22×C414yes—
432#125C22×C4116yes—
433#125C22×C4116yes—
434#125C22×C4116yes—
435#125C22×C418yes—
436#125C22×C4116yes—
437#125C22×C4116yes—
438#125C22×C4116yes—
439#125C22×C414yes—
440#125C22×C414yes—
441#124C22×C414yes—
442#124C22×C414yes—
443#124C22×C414yes—
444#124C22×C4116yes—
445#124C22×C418yes—
446#124C22×C4116yes—
447#124C22×C4116yes—
448#124C22×C418yes—
449#123C22×C418yes—
450#123C22×C418yes—
451#123C22×C418yes—
452#123C22×C4116yes—
453#123C22×C4116yes—
454#123C22×C4116yes—
455#123C22×C4116yes—
456#123C22×C4116yes—
457#123C22×C4116yes—
458#123C22×C4116yes—
459C22⋊Q8C22×C414yes—
460C22⋊Q8C22×C414yes—
461C22⋊Q8C22×C418yes—
462C22⋊Q8C22×C414yes—
463C22⋊Q8C22×C414yes—
464C22⋊Q8C22×C418yes—
465C22⋊Q8C22×C414yes—
466C22⋊Q8C22×C414yes—
467C22⋊Q8C22×C414yes—
468C22⋊Q8C22×C414yes—
469C22⋊Q8C22×C414yes—
470C22⋊Q8C22×C414yes—
471C22⋊Q8C22×C4116yes—
472C22⋊Q8C22×C418yes—
473C22⋊Q8C22×C4116yes—
474C22⋊Q8C22×C4116yes—
475C22⋊Q8C22×C418yes—
476C22⋊Q8C22×C4116yes—
477C22⋊Q8C22×C418yes—
478C22⋊Q8C22×C4116yes—
479C22⋊Q8C22×C4116yes—
480C22⋊Q8C22×C4116yes—
481C22⋊Q8C22×C4116yes—
482C22⋊Q8C22×C4116yes—
483#121C22×C414yes—
484#121C22×C414yes—
485#121C22×C414yes—
486#121C22×C414yes—
487#121C22×C414yes—
488#121C22×C414yes—
489#121C22×C4116yes—
490#121C22×C4116yes—
491#121C22×C418yes—
492#121C22×C4116yes—
493#121C22×C4116yes—
494#120C22×C418yes—
495C4×Q8C22×C414yes—
496C4×Q8C22×C414yes—
497C4×Q8C22×C418yes—
498C4×Q8C22×C418yes—
499C4×Q8C22×C418yes—
500C4×Q8C22×C4116yes—
501C4×Q8C22×C414yes—
502C4×Q8C22×C414yes—
503C4×Q8C22×C414yes—
504C4×Q8C22×C414yes—
505C4×Q8C22×C418yes—
506C4×Q8C22×C418yes—
507C4×Q8C22×C418yes—
508C4×Q8C2414yes—
509C4×Q8C2414yes—
510C4×Q8C2414yes—
511C4×Q8C2418yes—
512C4×Q8C24116yes—
513C4×Q8C2414yes—
514C4×D4C22×C418yes—
515C4×D4C22×C418yes—
516C4×D4C22×C418yes—
517C4×D4C22×C418yes—
518C4×D4C22×C414yes—
519C4×D4C22×C414yes—
520C4×D4C22×C414yes—
521C4×D4C22×C414yes—
522C4×D4C22×C4116yes—
523C4×D4C22×C4116yes—
524C4×D4C22×C4116yes—
525C4×D4C22×C418yes—
526C4×D4C22×C418yes—
527C4×D4C22×C418yes—
528C4×D4C2414yes—
529C4×D4C2418yes—
530C4×D4C2418yes—
531C4×D4C2414yes—
532C4×D4C24116yes—
533#117C22×C412yes—
534#117C22×C414yes—
535#117C22×C412yes—
536#117C22×C414yes—
537#117C22×C414yes—
538#117C22×C418yes—
539#117C22×C418yes—
540#117C22×C418yes—
541#117C22×C4116yes—
542#117C2414yes—
543#117C2414yes—
544#117C2414yes—
545#117C2418yes—
546#117C24116yes—
547C2×C4⋊C4C22×C414yes—
548C2×C4⋊C4C22×C418yes—
549C2×C4⋊C4C22×C414yes—
550C2×C4⋊C4C22×C418yes—
551C2×C4⋊C4C22×C4116yes—
552C2×C22⋊C4C22×C414yes—
553C2×C42C22×C411yescharacteristic
554C2×C42C22×C411yescharacteristic
555C2×C42C22×C411yescharacteristic
556C2×C42C22×C412yes—
557C2×C42C22×C411yescharacteristic
558C2×C42C2414yes—
559C2×C42C2412yes—
560C2×C42C2418yes—
561C2×C42C24116yes—
562C2×C42C2411yescharacteristic
563C2×C42C2412yes—
564C2×C42C2411yescharacteristic
565C4⋊C8C2414yes—
566C4⋊C8C2418yes—
567C4⋊C8C2414yes—
568C4⋊C8C2418yes—
569C4⋊C8C2414yes—
570C4⋊C8C2418yes—
571C4⋊C8C2418yes—
572C4⋊C8C24116yes—
573C4⋊C8C24116yes—
574C4⋊C8C24116yes—
575C4⋊C8C2418yes—
576C4⋊C8C2418yes—
577C4⋊C8C2418yes—
578C4⋊C8C2414yes—
579C4⋊C8C2414yes—
580C4⋊C8C2414yes—
581C4⋊C8C24116yes—
582C4⋊C8C2418yes—
583C4⋊C8C2418yes—
584C22⋊C8C2418yes—
585C22⋊C8C2418yes—
586C22⋊C8C2418yes—
587C22⋊C8C2418yes—
588C22⋊C8C2418yes—
589C22⋊C8C2418yes—
590C22⋊C8C24116yes—
591C22⋊C8C24116yes—
592#97C2418yes—
593#97C2418yes—
594#97C2418yes—
595#97C2418yes—
596#97C24116yes—
597#97C2418yes—
598#97C24116yes—
599C4×C8C2412yes—
600C4×C8C2412yes—
601C4×C8C2412yes—
602C4×C8C2412yes—
603C4×C8C2412yes—
604C4×C8C2412yes—
605C4×C8C2418yes—
606C4×C8C2418yes—
607C4×C8C24116yes—
608C4×C8C2418yes—
609C4×C8C24116yes—
610C4×C8C2412yes—
611C4×C8C2412yes—
612C4×C8C2418yes—
613C4×C8C2418yes—
614C24C23×C411yescharacteristic
615#41—28no—
616#41—28no—
617#41—48no—
618#41—48no—
619#41—416no—
620C2×Q8—48no—
621C2×Q8—416no—
622C2×Q8C23×C414yes—
623C2×Q8C23×C414yes—
624C2×Q8C23×C414yes—
625C2×Q8C23×C414yes—
626C2×Q8C23×C418yes—
627C2×Q8C23×C4116yes—
628C2×Q8C23×C414yes—
629C2×D4C23×C418yes—
630C2×D4C23×C414yes—
631C2×D4C23×C414yes—
632C2×D4C23×C418yes—
633C2×D4C23×C418yes—
634C2×D4C23×C414yes—
635C2×D4C23×C4116yes—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—44no—
639C22×C4C23×C411yescharacteristic
640C22×C4C23×C411yescharacteristic
641C22×C4C23×C411yescharacteristic
642C22×C4C23×C412yes—
643C22×C4C23×C412yes—
644C22×C4C23×C412yes—
645C22×C4C23×C418yes—
646C22×C4C23×C412yes—
647C22×C4C23×C412yes—
648C22×C4C23×C412yes—
649C22×C4C23×C418yes—
650C22×C4C23×C418yes—
651C22×C4C23×C4116yes—
652C22×C4C23×C4116yes—
653C22×C4C2518yes—
654C22×C4C2511yescharacteristic
655C22×C4C2511yescharacteristic
656C22×C4C2511yescharacteristic
657M16—28no—
658M16—28no—
659M16—216no—
660M16—44no—
661M16—44no—
662M16—48no—
663M16—416no—
664C2×C8—22no—
665C2×C8—24no—
666C2×C8—28no—
667C2×C8—22no—
668C2×C8—22no—
669C2×C8—22no—
670C2×C8—22no—
671C2×C8—216no—
672C2×C8—41no—
673C2×C8—42no—
674C2×C8—41no—
675C2×C8—48no—
676C2×C8—416no—
677C2×C82−1+414yes—
678C2×C8C2512yes—
679C2×C8C2518yes—
680C2×C8C2511yescharacteristic
681C2×C8C2511yescharacteristic
682C2×C8C2512yes—
683C2×C8C2518yes—
684C2×C8C2518yes—
685C2×C8C2511yescharacteristic
686C2×C8C2511yescharacteristic
687C4⋊C4C23×C414yes—
688C4⋊C4C23×C418yes—
689C4⋊C4C23×C414yes—
690C4⋊C4C23×C418yes—
691C4⋊C4C23×C418yes—
692C4⋊C4C23×C414yes—
693C4⋊C4C23×C414yes—
694C4⋊C4C23×C418yes—
695C4⋊C4C23×C414yes—
696C4⋊C4C23×C418yes—
697C4⋊C4C23×C4116yes—
698C4⋊C4C23×C4116yes—
699C4⋊C4C23×C418yes—
700C4⋊C4C23×C418yes—
701C4⋊C4C23×C4116yes—
702C4⋊C4C23×C414yes—
703C4⋊C4C23×C414yes—
704C4⋊C4C23×C418yes—
705C4⋊C4C23×C414yes—
706C4⋊C4C23×C4116yes—
707C4⋊C4C23×C418yes—
708C4⋊C4C23×C418yes—
709C4⋊C4C23×C414yes—
710C4⋊C4C23×C414yes—
711C4⋊C4C23×C418yes—
712C4⋊C4C23×C4116yes—
713C4⋊C4C23×C418yes—
714C4⋊C4C23×C4116yes—
715C22⋊C4C23×C414yes—
716C22⋊C4C23×C418yes—
717C22⋊C4C23×C414yes—
718C22⋊C4C23×C418yes—
719C22⋊C4C23×C418yes—
720C22⋊C4C23×C418yes—
721C22⋊C4C23×C418yes—
722C22⋊C4C23×C418yes—
723C22⋊C4C23×C418yes—
724C22⋊C4C23×C4116yes—
725C22⋊C4C23×C4116yes—
726C22⋊C4C23×C418yes—
727C22⋊C4C23×C418yes—
728C22⋊C4C23×C4116yes—
729C22⋊C4C23×C418yes—
730C22⋊C4C23×C4116yes—
731C42C23×C411yescharacteristic
732C42C23×C412yes—
733C42C23×C411yescharacteristic
734C42C23×C412yes—
735C42C23×C412yes—
736C42C23×C412yes—
737C42C23×C411yescharacteristic
738C42C23×C411yescharacteristic
739C42C23×C418yes—
740C42C23×C418yes—
741C42C23×C414yes—
742C42C23×C414yes—
743C42C23×C4116yes—
744C42C23×C4116yes—
745C42C2512yes—
746C42C2512yes—
747C42C2518yes—
748C42C2518yes—
749C23—22no—
750C23—42no—
751C23C24×C411yescharacteristic
752C23C24×C411yescharacteristic
753C23C24×C418yes—
754C23C24×C411yescharacteristic
755Q8—28no—
756Q8—28no—
757Q8—28no—
758Q8—28no—
759Q8—416no—
760Q8—48no—
761Q8—44no—
762D4—216no—
763D4—28no—
764D4—28no—
765D4—44no—
766D4—48no—
767D4—416no—
768D4—48no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—28no—
773C2×C4—28no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—216no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—48no—
786C2×C4—416no—
787C2×C4—48no—
788C2×C4—416no—
789C2×C4C24×C412yes—
790C2×C4C24×C418yes—
791C2×C4C24×C411yescharacteristic
792C2×C4C24×C411yescharacteristic
793C2×C4C24×C412yes—
794C2×C4C24×C418yes—
795C2×C4C24×C418yes—
796C2×C4C24×C418yes—
797C2×C4C24×C412yes—
798C2×C4C24×C418yes—
799C2×C4C24×C411yescharacteristic
800C2×C4C24×C412yes—
801C2×C4C2×2−1+412yes—
802C2×C4#58512yes—
803C2×C4C2611yescharacteristic
804C8—21no—
805C8—21no—
806C8—28no—
807C8—22no—
808C8—22no—
809C8—28no—
810C8—28no—
811C8C2×2−1+412yes—
812C8C2×2−1+412yes—
813C22—22no—
814C22—28no—
815C22—22no—
816C22—22no—
817C22—28no—
818C22—21no—
819C22—21no—
820C22—28no—
821C22—44no—
822C22C4×2−1+412yes—
823C22C25×C411yescharacteristic
824C4—22no—
825C4—22no—
826C4—28no—
827C4—22no—
828C4—28no—
829C4—28no—
830C4—28no—
831C4—21no—
832C4—21no—
833C4—28no—
834C4C4×2−1+412yes—
835C4#357314yes—
836C4C22×2−1+411yescharacteristic
837C4C2×#58511yescharacteristic
838C2—22no—
839C2—48no—
840C2—41no—
841C2—41no—
842C2C2×C4×2−1+411yescharacteristic
843C2C2×#357312yes—
subgroupG/H
centerC2×C8C25
commutator, socleC22C25×C4
Frattini, cosocleC2×C4C26
prime radical#62761C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C8 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #60338C2semidirect
3. #60337C2semidirect
4. #60336C2semidirect
5. #60332C2semidirect
6. #60331C2semidirect
7. #60330C2semidirect
8. #60275C2semidirect
9. #60267C2semidirect
10. #60266C2semidirect
11. #60254C2semidirect
12. #60249C2semidirect
13. #60218C2semidirect
14. #60206C2semidirect
15. #60204C2semidirect
16. Q8×#131C2semidirect
17. C2×#2960C2semidirect
37. #2995C22semidirect
39. #2994C22semidirect
42. #2993C22semidirect
44. #2992C22semidirect
47. #2990C22semidirect
49. #2989C22semidirect
51. #2987C22semidirect
53. #2986C22semidirect
55. #2985C22semidirect
56. #2985C22semidirect
57. #2984C22semidirect
58. #2983C22semidirect
59. #2971C22semidirect
60. #2969C22semidirect
61. #2969C22semidirect
70. #2966C22semidirect
71. #2966C22semidirect
76. C8×#41C22semidirect
79. Q8×M16C22semidirect
82. #2962C22semidirect
83. #2962C22semidirect
94. #2960C22semidirect
95. #2960C22semidirect
98. C2×C8×Q8C22semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#627612
#603382
#603372
#603362
#603322
#603312
#603302
#602752
#602672
#602662
#602542
#602492
#602182
#602062
#602042
Q8×#1312
C2×#29602